Math ClubVolume of Balls: from $$R^n$$ to Infinite DimensionsMarco Carfagnini (UConn)

Wednesday, February 19, 2020
5:45pm – 6:35pm

Storrs Campus
Monteith 314

How do we find the volume of a ball in an $$n$$-dimensional space? We will see how techniques from multivariable calculus can be generalized to answer this question. Surprisingly, as the dimension gets higher, the volume gets smaller and smaller! By briefly discussing infinite-dimensional spaces and some functional analysis, we will see why that is not surprising at all! The talk will make use of integration over plane and solid regions as a starting point, so some familiarity with double and triple integrals as in multivariable calculus is a useful prerequisite.

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